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MIT OpenCourseWareMIT 18.02SC Multivariable Calculus, Fall 2010 (2010)

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Instructor: Christine Breiner, David Jordan, Joel Lewis

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

View the complete course: http://ocw.mit.edu/18-02SCF10



This movie is part of the collection: MIT OpenCourseWare

Producer: MIT OpenCourseWare
Audio/Visual: sound, color
Language: English
Keywords: multivariable calculus, vectors, matrices, partial derivatives, double integrals, line integrals, triple integrals, surface integrals

Creative Commons license: Attribution-Noncommercial-Share Alike 3.0


Individual Files

Movie Files Thumbnail Animated GIF MPEG4 Ogg Video 512Kb MPEG4
Coordinate free proofs: centroid of a triangle 3.3 KB 
273.9 KB 
24.6 MB 
49.9 MB 
47.7 MB 
Dot products and angles 4.0 KB 
217.5 KB 
19.3 MB 
39.5 MB 
37.2 MB 
Components of a vector 3.4 KB 
128.5 KB 
11.2 MB 
22.7 MB 
21.7 MB 
Area of a parallelogram 3.5 KB 
79.9 KB 
7.5 MB 
13.3 MB 
14.5 MB 
Determinants 3.9 KB 
112.9 KB 
10.3 MB 
18.9 MB 
20.0 MB 
Volume of a parallelepiped 3.9 KB 
67.2 KB 
6.4 MB 
10.7 MB 
12.5 MB 
Finding area using cross products 3.9 KB 
129.1 KB 
11.1 MB 
19.4 MB 
21.6 MB 
Matrix multiplication practice 2.8 KB 
246.0 KB 
23.4 MB 
38.8 MB 
45.3 MB 
Solve a linear system using matrices 3.1 KB 
211.9 KB 
39.5 MB 
68.2 MB 
76.9 MB 
Equations of planes 3.5 KB 
326.7 KB 
30.2 MB 
62.2 MB 
58.8 MB 
Distance of a point to a plane 3.2 KB 
195.7 KB 
18.2 MB 
37.1 MB 
35.1 MB 
Systems of linear equations 3.8 KB 
306.5 KB 
26.3 MB 
54.2 MB 
51.0 MB 
Parametrized lines and intersections 3.1 KB 
205.9 KB 
18.7 MB 
36.1 MB 
36.4 MB 
Parametric line intersecting a plane 3.4 KB 
194.3 KB 
17.7 MB 
34.6 MB 
34.4 MB 
Differentiating a vector valued function 3.7 KB 
326.9 KB 
31.0 MB 
55.3 MB 
59.8 MB 
Parametric curves: velocity, acceleration, length 3.1 KB 
195.5 KB 
18.2 MB 
36.0 MB 
35.4 MB 
Graphing surfaces 2.8 KB 
191.5 KB 
17.2 MB 
31.2 MB 
33.4 MB 
Level curves 3.4 KB 
246.1 KB 
22.9 MB 
44.8 MB 
44.3 MB 
Level curves and critical points 3.4 KB 
202.3 KB 
18.4 MB 
35.6 MB 
35.7 MB 
Partial derivatives 2.9 KB 
121.7 KB 
11.7 MB 
22.5 MB 
22.6 MB 
Tangent plane approximation 3.6 KB 
154.0 KB 
15.2 MB 
26.2 MB 
29.4 MB 
Least squares 3.6 KB 
220.5 KB 
19.9 MB 
35.3 MB 
38.5 MB 
Second derivative test 3.1 KB 
207.7 KB 
18.9 MB 
37.8 MB 
36.8 MB 
Max/Min 3.1 KB 
336.8 KB 
30.6 MB 
60.4 MB 
59.5 MB 
Total differentials and the chain rule 3.2 KB 
265.2 KB 
25.5 MB 
46.0 MB 
49.2 MB 
Tangent planes 3.2 KB 
218.6 KB 
19.8 MB 
40.3 MB 
38.4 MB 
Gradient and directional derivative 3.4 KB 
326.4 KB 
29.7 MB 
59.4 MB 
57.7 MB 
Lagrange multipliers 3.6 KB 
254.7 KB 
22.5 MB 
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Lagrange multipliers (3 variables) 3.2 KB 
328.5 KB 
29.0 MB 
56.5 MB 
56.4 MB 
The chain rule with constraints 3.2 KB 
175.4 KB 
33.8 MB 
62.4 MB 
65.0 MB 
Gradients - composition 3.5 KB 
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38.6 MB 
43.9 MB 
Regions of integration 3.3 KB 
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39.0 MB 
75.3 MB 
75.7 MB 
Changing the order of integration 2.6 KB 
141.6 KB 
13.2 MB 
25.9 MB 
25.8 MB 
Integration in polar coordinates 2.8 KB 
194.2 KB 
38.2 MB 
64.4 MB 
74.8 MB 
Integrals with density 3.4 KB 
176.9 KB 
33.9 MB 
59.3 MB 
66.2 MB 
Change of variables 3.6 KB 
224.8 KB 
20.4 MB 
36.0 MB 
39.2 MB 
Integral of exp(-x^2) 2.9 KB 
223.6 KB 
20.9 MB 
34.5 MB 
40.7 MB 
Change of variables 2.8 KB 
229.6 KB 
43.7 MB 
76.6 MB 
84.7 MB 
Line integrals: path dependence 3.2 KB 
177.9 KB 
34.3 MB 
62.2 MB 
66.1 MB 
Line integrals: parametrization independence 3.4 KB 
298.3 KB 
27.4 MB 
54.0 MB 
53.3 MB 
Line integrals by geometric reasoning 4.0 KB 
258.7 KB 
23.3 MB 
47.7 MB 
44.9 MB 
Fundamental theorem of line integrals 3.8 KB 
269.3 KB 
24.3 MB 
47.9 MB 
47.3 MB 
Non-conservative vector fields 3.5 KB 
236.0 KB 
21.8 MB 
42.2 MB 
42.5 MB 
Potentials of gradient fields 3.1 KB 
246.3 KB 
24.9 MB 
43.2 MB 
48.3 MB 
Green's Theorem: an off center circle 3.1 KB 
178.2 KB 
16.4 MB 
30.7 MB 
31.9 MB 
Green's Theorem: area under an arch 4.0 KB 
198.1 KB 
18.8 MB 
34.5 MB 
36.3 MB 
Application of Green's theorem 3.6 KB 
163.8 KB 
15.8 MB 
27.7 MB 
30.6 MB 
Flux across a curve 4.5 KB 
329.2 KB 
31.6 MB 
58.4 MB 
61.3 MB 
Green's Theorem in normal form 3.8 KB 
272.0 KB 
24.2 MB 
48.1 MB 
46.9 MB 
Extended Green's Theorem 3.7 KB 
267.9 KB 
50.8 MB 
99.8 MB 
99.2 MB 
Domains of vector fields 3.0 KB 
321.2 KB 
30.1 MB 
52.6 MB 
58.2 MB 
Volume in cylindrical coordinates 3.2 KB 
216.0 KB 
39.8 MB 
76.8 MB 
77.0 MB 
Average height 4.0 KB 
362.8 KB 
31.9 MB 
66.8 MB 
62.2 MB 
Moment of inertia of a cylinder 3.8 KB 
250.5 KB 
21.8 MB 
45.2 MB 
42.4 MB 
Average distance on a sphere 4.6 KB 
326.7 KB 
28.4 MB 
54.5 MB 
55.1 MB 
Gravity and a half-sphere 3.0 KB 
248.5 KB 
24.5 MB 
47.5 MB 
47.8 MB 
Flux through easy surfaces 3.6 KB 
154.6 KB 
15.0 MB 
26.1 MB 
28.8 MB 
Flux through a square 3.2 KB 
232.1 KB 
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36.9 MB 
42.6 MB 
Flux through surfaces 4.5 KB 
263.4 KB 
24.7 MB 
46.7 MB 
48.2 MB 
Flux 3.8 KB 
264.5 KB 
24.7 MB 
48.9 MB 
48.0 MB 
Flux and the divergence theorem 3.6 KB 
293.0 KB 
26.1 MB 
51.9 MB 
50.9 MB 
Extended Gauss' Theorem 3.1 KB 
228.8 KB 
41.4 MB 
84.6 MB 
80.4 MB 
Del and the product rule 3.5 KB 
204.0 KB 
18.6 MB 
35.6 MB 
36.0 MB 
Line integral on a helix 3.0 KB 
244.9 KB 
24.5 MB 
48.7 MB 
47.8 MB 
Conservative fields and exact differentials 3.5 KB 
333.8 KB 
32.3 MB 
64.7 MB 
63.2 MB 
Stokes' Theorem 3.5 KB 
206.3 KB 
38.5 MB 
78.9 MB 
74.7 MB 
Extended Stokes' Theorem 3.5 KB 
183.4 KB 
34.5 MB 
70.5 MB 
66.5 MB 
Simply connected regions 2.9 KB 
320.4 KB 
32.3 MB 
62.4 MB 
62.9 MB 
More Stokes' Theorem 3.6 KB 
197.8 KB 
18.3 MB 
37.2 MB 
35.4 MB 
Consequences of Stokes' Theorem 4.0 KB 
263.6 KB 
24.3 MB 
50.2 MB 
47.8 MB 
Information FormatSize
MIT18_02SCF10_files.xml Metadata [file] 
MIT18_02SCF10_meta.xml Metadata 1.3 KB 

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